Decaying Majoron DM and Structure Formation kingman Cheung - PowerPoint PPT Presentation

Decaying Majoron DM and Structure Formation kingman Cheung September 11 2019 TAUP

References Majoron DM: Berezinsky and Valle, PLB318 (1993), 360 CMB constraint: Lattanzi, Riemer-Sørensen, Tortola, Valle, 
 PRD 88 (2013) 063528 Structure Formation: Kuo, Lattanzi, KC, Valle, JCAP 1812 
 (2018) 12 



 Lambda Cold Dark Matter Model ❖ Standard model of Cosmology. Dark matter consists of unknown elementary particle(s), produced in early universe, that is “cold” — velocity dispersion on structure formation is negligible. 
 ❖ Explains structure formation for large scales: 
 with small density fluctuations normalised to the observed CMB and allowed 
 to grow via gravitational instability, can account for many properties of structures a 
 t most well- observed scales and epochs. On scales larger than about 10 kpc, 
 the predictions of Λ CDM have been successful. 
 Yet, for scale smaller than 10 kpc, inconsistent with observations . 
 ❖ Missing satellite problem, the too-big-to-fail problem, the cusp-core problem. 


Cusp-Core Problem ❖ LCDM simulations predict DM density cusp in center of galaxies, but inconsistent with observations. ❖ Especially low-mass galaxies.

A Few Possible Solutions ❖ Baryon physics: efficiency of transforming baryons into stars to be lower in lower-mass systems. ❖ Some warm DM: its thermal velocity dispersion provides free streaming that suppresses low-mass halos or sub-halos, and also reduce the density cusp at the center. ❖ DM has self-interactions, reducing the density cusp, form less sub- halos. ❖ Fuzzy dark matter: large de Broglie wavelength suppresses 
 small-scale structures (Hu et al.).


 Outline 1. Warm DM with relativistic properties can alleviate 
 the small-scale crisis. Majoron DM is warm. 
 2. In addition, majoron DM can decay into neutrinos: 
 J → νν with a life-time of order of the age of the Universe. 
 3. CMB provides a strong constraint on majoron DM 
 life-time, in order to avoid producing too much 
 fluctuation power on the largest CMB scales. 
 4. We investigate the WARM and DECAY nature of 
 majoron DM on structure formation.

Majoron Physics The seesaw mechanism involves spontaneously broken 
 lepton number symmetry, involves a singlet scalar 
 coupling to singlet neutrino: λσν cT L τ 2 ν c ⟨ σ ⟩ ≡ v 1 L , v 1 can be large to give a large majorana mass. So the mass 
 matrix for left- and right-handed neutrino is " # Y 3 v 3 Y � v 2 M � ¼ Y � T v 2 Y 1 v 1 v 2 2 m ν = Y 3 v 3 − Y ν Y − 1 1 Y T ν v 1

v 3 (v 2 ) is the VEV of the Higgs triplet (doublet). 
 Since the lepton-number symmetry is spontaneously 
 broken, there is Nambu-Goldstone boson: J ∝ v 3 v 2 2 ℑ ( Δ 0 ) − 2 v 2 v 2 3 ℑ ( Φ 0 ) + v 1 ( v 2 2 + 4 v 2 3 ) ℑ ( σ ) In principle, J is massless but acquires a mass via non- 
 perturbative gravitational effect. m J ≃ O (keV)

J mainly decays into light neutrinos via m ν i 2 J ∑ ℒ Y = i ν T g ij = − i g ij τ 2 ν j + h . c . δ ij v 1 ij Decay width into neutrinos is ∑ i m 2 Γ J → νν = m J ν i 2 v 2 32 π 1 Subleading decay into a pair of photons: 2 Γ J → γγ = α 2 m 3 2 v 2 3 ) m 2 J 3 J ∑ ( − 2 T f N f Q 2 f 64 π 3 v 2 12 m 2 2 v 1 f f

Structure Formation

Goal of this study We examine the effect of decaying warm dark matter on non-linear structure formation, due to two effects (1) Warm nature (free streaming) of the majoron DM (2) Decay of majoron DM

Abbreviations Initial Conditions Lifetime WDM mass SCDM CDM N/A ∞ DCDM CDM N/A 50 Gyr SWDM-M WDM 1 . 5 keV ∞ DWDM-M WDM 50 Gyr 1 . 5 keV SWDM-m WDM 0 . 158 keV ∞ DWDM-m WDM 50 Gyr 0 . 158 keV Table 1 . The abbreviations and features of the simulations we have performed in this article. To avoid word cluttering in the following we will use these abbreviations.

We use two values for m J = 0.158 eV and 1.5 eV and lifetime τ = 50 Gyr or ∞ • The lighter one is for thermal DM production 
 • the heavier one is for non-thermal history or based on thermal production but later diluted by additional entropy after decoupling. • The lifetime from CMB constraint is 50 Gyr. We 
 also study the stable DM case.

Remarks: • The lighter mass 0.158 keV gives the correct relic 
 density as a scalar particle that decouples in early 
 Universe. 
 • Both values are in tension with the lower limit from 
 Lyman-alpha, m J > 3.5 keV . Nevertheless, the limit is 
 model dependent, e.g., IGM thermal history. 
 • If m J = 5.3 keV is chosen, it is almost no different from CDM. 
 • The lighter value is chosen so as to maximize the 
 free streaming effects. And it mainly decays into neutrinos. 
 • Here we only investigate the effects of free streaming and 
 decays, not the exact mass limit from structure formation.

Simulation of Decaying particle • We concern with decay of DM into relativistic neutrinos • The mass of “simulation particles” is reduced by a small 
 amount at each time step due to decay of DM: M ( t ) = M (1 − R + R e − t ( z ) / τ J ) , mass of the simulation particles , and where R ≡ ( Ω M − Ω b )/ Ω M is the DM fraction • In addition to reducing simulation particle mass, 
 the expansion rate of the Universe also modified 
 according to the energy content at each z

The evolution of DM and decay product is described by ρ dm + 3 H ρ dm = − a ˙ ρ dm , τ J ρ dp + 4 H ρ dp = a ˙ ρ dm , τ J H and a are the conformal Hubble parameter and scale factor. 
 The Hubble parameter at each red-shift is H H 2 ( z ) = 8 π G a 2 ( ρ dm ( z ) + ρ b ( z ) + ρ dp ( z ) + ρ Λ ( z )) , 3 ρ b , ρ Λ are unaffected by energy exchange between DM and dp, so 
 • they evolve in standard way: ρ b ∝ a − 3 , ρ Λ ∝ const

• Further assumption: contribution of decay product dp to energy 
 density is very small, due to long lifetime of majoron. 
 • The decay product, neutrinos, are free streaming and do not cluster. 
 • The decay is to reduce the amount of matter that is able to cluster. 
 But we expect this assumption to break down on the largest scale 
 above the free-streaming length, which is the size of horizon scale 
 much larger than our simulation size. 
 ρ dm , ρ dp • Given initial conditions for we solve for the evolution equations 
 and calculate the Hubble parameter at each time-step


 
 Initial Conditions ❖ Use linear theory to evolve the primordial perturbation in k space to some initial redshift z = 99, which is well before the DM decays, so decaying DM and stable DM have the same initial condition. 
 ❖ In WDM, we estimate the initial power spectrum as 
 
 P WDM ( k ) = T 2 WDM ( k ) × P CDM ( k ) , where transfer function T WDM (k) 1 + ( α k ) 2 ν � � 5 / ν , � T WDM ( k ) = � � where α = 0 . 048( Ω DM / 0 . 4) 0 . 15 ( h/ 0 . 65) 1 . 3 (keV /m DM ) 1 . 15 (1 . 5 /g ) 0 . 29 Mpc and ν = 1 . 2 . is the dark matter energy density, m ⌘ m is the dark matter mass and g is Ω

Initial matter power spectra for CDM and WDM using 2LTPic code. 
 Power spectrum drops to 1/ e of CDM at k ≈ 1 (0.158 keV) and 
 17h (1.5 keV). These are roughly the free-streaming wave numbers.

Simulation Details 
 • starts at z = 99 • both stable and decaying DM exact same initial 
 conditions and same random seed. • For WDM simulations, thermal velocity at z=99 was input 
 to simulation particles consistent with initial spectrum. • Other cosmological parameters: Ω m = 0.3, Ω Λ = 0.7, Ω b = 0.04; h = 0.7, n s = 0.96, σ 8 = 0.8 • Use 512 3 simulation particles in a cube with side 50 h -1 Mpc • M sim ≈ 7 .8 10 7 h -1 M sun . • Periodic boundary condition.

Simulation Results Density Fields

Density field: M: 1.5 keV , m: 0.158 keV 1 + δ = ρ / ¯ ρ

Stable / Decay log 10 ( ρ S / ρ D ) = log 10 [( δ S + 1)exp( t 0 / τ J )] − log 10 ( δ D + 1)

Matter Power Spectrum

Matter Power Spectrum comparison

Interpretations • Effects of decay is more obvious at low z • Compare SCDM with SWDM-(M,m), at large scale (small k) 
 are very close, but differ at small scale (large k), due to 
 free-streaming of WDM. • Free-streaming of m J =1.5 keV is really small. • Compare DWDM-M and DWDM-m, free-streaming effect still 
 there for small scale suppression. • Further suppression at all scales due to decay, which do not 
 show strong dependence on scales. In contrast to free- 
 streaming effect of WDM.

Ratio of matter power spectrum

• The decay suppresses the matter power at all scales. • The suppression due to decay is more obvious at small scale. • The suppression due to decay gradually decreases toward 
 large scale. All curves converge to the same value as beyond 
 free-streaming length CDM and WDM behave the same. • Nonlinear enhancement of the effect of decay on small scales 
 is stronger for lighter WDM. There is a sharp drop for 
 m J =0.158 keV near the free-streaming length scale.

Halo Mass Function